Application des groupes de Lie {\`a} la recherche des sym{\'e}tries des tissus implicites du plan

TL;DR

This paper explores the application of Lie group theory to identify symmetries in implicit planar webs, linking algebraic structures to geometric properties and extending previous results in web symmetry analysis.

Contribution

It revisits Alain H{é}naut's work within the Lie group framework and establishes a connection between fabric symmetry Lie algebras and Darboux polynomials.

Findings

Lie group actions effectively characterize web symmetries.

A relationship between Lie algebra of symmetries and Darboux polynomials is demonstrated.

The approach provides new insights into the structure of implicit planar webs.

Abstract

Alain H{\'e}naut's results on implicit web symmetry groups are revisited in the usual framework of Lie group actions on differential equations. A link is also given between the Lie algebra of fabric symmetries and the existence of Darboux polynomials.